ASTRONOMY 9: HISTORY OF COSMOLOGY

Handout #24

J. E. Baker
UC Berkeley, Spring 2000

The Cosmic Microwave Background (CMB)

• Observational Discovery
  • 1941: Adams and McKellar measure ``temperature of space'' to be about 2.3 K (significance not realized until 1965)
  • Arno Penzias and Robert Wilson (Bell Labs, NJ)
  • 1964: Detect faint excess noise in a radio antenna horn, $T\approx 3.5$ K
  • 1965: Great efforts to identify the source, even scraping off the pigeon droppings!
  • 1978: Penzias and Wilson awarded Nobel Prize for discovery of the cosmic background
• Interpretation
  • Gamow and collaborators (1948, 1953): relic microwave radiation from the Big Bang should permeate the universe, $T\approx 5$ K (largely unknown)
  • Russian cosmologists (early 60s) suggest looking for this radiation (not noticed nor pursued)
  • Princeton cosmologists (Peebles) independently discover and improve on Gamow's result
  • Dicke, Roll, and Wilkinson (Princeton) start constructing a receiver in 1964 to look for the CMB
  • Learn of Penzias and Wilson's problem, and realize they have seen the CMB!
  • CMB is a ``fossil relic'' of an early time when the universe was hot and dense, the ``echo'' of the Big Bang
  • Recall that looking out in space is looking back in time
  • Eventually, arrive at a point where the universe becomes opaque: a ``wall'' behind which we cannot see
    • This happens when electrons and protons first combine to form neutral hydrogen
    • Free electrons can absorb lots of different wavelengths of light, so dense early universe was opaque
    • Bound electrons can only absorb special wavelengths, so universe later becomes (mostly) transparent
    • Transition occurs at $z\approx 1100$, $T\approx 10^4$ K, $t\approx$ 300,000 years
    • Radiation at this time was mostly optical/UV, redshifted by factor of 1100 as universe expands, so becomes microwave ( $\lambda\approx 3$ mm)
  • Note CMB contributes about 1% of TV ``static''
  • CMB is very difficult to interpret as anything other than a remnant of the big bang: death of steady state theory!
• Learning about Cosmology from the CMB
  • The CMB is very smooth (isotropic), almost exactly the same temperature in all directions
  • So the matter in the universe was also very smooth, almost exactly the same density at all locations
  • Only later do the tiny inhomogeneities develop into stars, galaxies, clusters of galaxies, etc.
  • Doppler Anisotropy
    • Note there is a special frame of rest defined by the CMB!
    • If you are moving with respect to this frame, can always tell, because CMB will look hotter (shorter $\lambda$) ahead of you and colder behind you (Doppler effect)
    • Earth has a motion of several hundred km/s, leads to temperature difference of about 1 part in 10<sup>-3</sup>
    • First measured in 1970s, no cosmological significance
    • Easy to subtract the Doppler pattern, look for original anisotropies imprinted in the background
  • Search for Anisotropy
    • Anisotropies (except Doppler) reflect tiny density variations in the early universe, sound waves traveling through the baryons (ordinary matter)
    • Ground-based experiments could not detect any anisotropy down to 1 part in 10<sup>5</sup>!
    • Problem for early ideas about galaxy formation: needed 1 part in 10<sup>3</sup>
    • Resolution: most of the mass is non-baryonic (weird, does not interact with CMB photons) dark matter
      • Normal matter (baryons) is prevented from growing into condensed structures by CMB radiation
      • Dark matter can start to grow earlier, so initial variations can be smaller
      • Lots of other evidence for dark matter, too...
      • Baryons (normal matter) only make up $<30\%$ of total!
  • COBE satellite (1989-1992)
    • Cosmic Background Explorer
    • Measures perfect blackbody spectrum for CMB, just as predicted! T=2.728 K
    • Finally detects variations in the temperature at level of 1 part in 10<sup>5</sup>
    • ``Seeds'' of the structures in the universe today!
    • Makes a map of (almost) the whole sky, but low resolution (blurry)
  • Measuring the curvature of the universe
    • Can predict exactly how big the sound waves in the early universe should be when universe becomes transparent
    • Measure the spectrum of these waves, and compare to prediction
    • If space is curved, acts like a lens
      • If geometry is flat, typical structures should look about $1^\circ$ in size
      • If geometry is spherical (closed), light rays converge, makes the structures look bigger
      • If geometry is hyperbolic, light rays diverge, makes structures look smaller
    • Define $\Omega_m$ to be the matter density as a fraction of the critical density: $\Omega_m = \rho/\rho_c$
    • If there is no $\Lambda$, $\Omega_m > 1$ means spherical and recollapse, $\Omega_m < 1$ means hyperbolic and expand forever, $\Omega_m = 1$ means flat and expand forever
    • Similarly, there is $\Omega_\Lambda$ for the fraction of the critical energy density contributed by $\Lambda$
    • Geometry is determined by total $\Omega_m + \Omega_\Lambda$ (+ $\Omega$'s for anything else in the universe)
    • If there is $\Lambda$, geometry does not determine fate
  • BOOMERANG (Antarctic balloon telescope)
    • Recently made high-resolution image of CMB (in a small part of sky)
    • Gets strong constraint that total $\Omega$ is close to 1, universe is (nearly) flat!
    • Combine with data from supernovae
      • With $\Lambda$, distant supernovae at a given z should be more distant (so look fainter) than if no $\Lambda$
      • 1998 result of the year: supernovae do show strong evidence for an accelerating universe!
  • Future
    • Ground-based telescopes in high desert sites will improve constraints on cosmological models
    • Satellites over the next decade (MAP, PLANCK) will obtain sharp images of the CMB over the whole sky!
    • May be able to pin down precisely what kind of cosmological model applies to our universe
    • We will understand the state of the universe at $z\approx 1100$ extremely well
    • Cosmologists will turn attention to later times (how do galaxies form?) and earlier times (towards the creation itself)
  • Current best model for the universe
    • $\Omega_m\approx 0.3$, $\Omega_\Lambda\approx 0.7$ (flat) seems consistent with most data
    • If $\Lambda$ does not do something strange in the future, universe will continue to expand forever!
    • Future is infinite, but will be very bleak if acceleration continues
• Why is the sky dark at night?
  • Actually a very profound question!
  • Rules out old idea of infinite static universe with infinitely old stars
  • Called ``Olbers' paradox'' (1820s), but known since Kepler
  • Every line of sight should intersect surface of a star, so sky should be as bright as the sun!
  • Two main reasons why this is not the case (first is most important):

    1.

    Observable part of the universe is finite since light travels at finite speed and universe has finite age (and/or is expanding), so most lines of sight do not intersect a star (yet)

    2.

    Energy from distant stars is redshifted by expansion

  • With the CMB there is another answer: the sky is bright! (If you had microwave eyes, or went back in time to $z\approx 1000$)
    • In this case it is the expansion that resolves the ``paradox''
• The Universe and the Heat Death
  • 2nd law of thermodynamics says entropy increases
  • Late 19th c. physicists figured the universe must be ``winding down'', on its way to heat death
  • But entropy contained in CMB is much larger than that being generated by stars, people, etc.
  • Measured roughly by ratio of number of photons to number of particles of ordinary matter (baryons): $\eta\approx 10^9$
  • So actually, the heat death has already mostly happened!
  • From nucleosynthesis calculation of deuterium abundance, we get $\Omega_B h^2\approx 0.02$ where h=H₀/(100 km/s/Mpc) and $\Omega_B$ is fraction of critical density contributed by baryons
  • If $h\approx 0.7$ then $\Omega_B$ is only 4%
  • Much evidence suggests that total matter density is between 20% and 40% of critical, so must be a lot of weird (non-baryonic) matter!

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